Property not inherited

A property assumed to pass to subobjects, quotients, or through a chain. It does not.

Would you have fallen for these?

Each is a real option from a previous-year paper. Read it cold and decide before opening it.

• Option D

  (11/9)X ~ Poisson(11/12)

  Why this is wrong, and why it looks right

  False. Scaling a Poisson variable does not give a Poisson variable: (11/9)X takes values 0, 11/9, 22/9, … which are not non-negative integers, so it cannot have any Poisson distribution. The Poisson family is closed under addition of independent variables, not under multiplication by constants.

  From this question

  Suppose X ~ Poisson(3/4). Then which of the following statements is true?

  See the full question

  Part B · december 2023 · free

• Option D

  F(x) has at most one real root.

  Why this is wrong, and why it looks right

  False. It reads the root count of f across to F, but a property of a function need not survive antidifferentiation. With $f=x^3+x$ and C = −1, SymPy gives F two real roots, $\pm \sqrt{\sqrt{5}-1}$.

  From this question

  Let f(x) be a cubic polynomial with real coefficients. Suppose that f(x) has exactly one real root and that this root is simple. Which one of the following statements holds for ALL antiderivatives F(x) of f(x)?

  See the full question

  Part B · december 2023

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